Optical element of multilayered thin film for X-rays and neutrons

ABSTRACT

This invention relates to novel methods of producing flat and curved optical elements with laterally and depth graded multilayer thin films, in particular multilayers of extremely high precision, for use with soft and hard x-rays and neutrons and the optical elements achieved by these methods. In order to improve the performance of an optical element, errors in d spacing and curvature are isolated and subsequently compensated.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. application Ser. No.:08/283,610, Filed Aug. 1, 1994, now abandoned.

BACKGROUND AND SUMMARY OF THE INVENTION

This invention relates to novel methods of producing flat and curvedoptical elements, in particular elements of extremely high precision,using multilayer thin films for use with soft and hard x-rays, cold andthermal neutrons, and the optical elements achieved by these methods.

Thin film technology has been widely used to control the reflection andtransmission of visible light. However, in the wavelength range ofx-rays and neutrons the use of thin films has only recently becomepracticable. X-ray and neutron optics has presented many challenges toscientists including the inability to reflect at near-normal incidence,poor quality of paraboloid or hyperboloid optical elements used forgrazing reflection and lack of sources. Recent advances in the qualitycontrol of Layered Synthetic Microstructures (LSM), or multilayers,allows the use of these structures as x-ray and neutron mirrors.

X-ray diffraction from multilayer mirrors is analogous to x-raydiffraction from perfect crystals where the lattice planes are locatedin the nodes of the standing wave produced by the superposition ofincident and reflected (diffracted) waves for enhanced diffractionefficiency. Multilayer mirrors can be considered as an extension ofnatural crystals for larger lattice spacings. Therefore, as forcrystals, x-ray photons will be reflected from multilayer structuresonly if the Bragg equation is met:

    nλ=2d sin (θ)

where

λ=wavelength of the incident radiation

d=layer-set spacing of a Bragg structure, or the lattice spacing of acrystal

θ=angle of incidence

n=the order of the reflection

The structure of a crystalline solid, a regular three dimensional arrayof atoms, forms a natural diffraction grating for x-rays. The quantity din the Bragg equation is the perpendicular distance between the planesof atoms in the crystal. The construction of an artificial diffractiongrating with a spacing on the order of the x-ray wavelength wasimpossible at the time W. L. Bragg derived his foundational equation.However, crystalline structure can now be imitated by thin filmmultilayers, so x-ray diffraction is no longer limited to structureswith naturally occurring d spacings.

In order for a multilayer structure to reflect by imitating a crystalstructure, a light element of the lowest possible electron density islayered with a heavy element of the highest possible electron density.The heavy element layer acts like the planes of atoms in a crystal, as ascatterer, while the light element layer behaves like the spacersbetween the planes of atoms. A further requirement of these two elementsis that they do not interdiffuse.

Multilayers possess advantages over natural crystalline structuresbecause by choosing the d spacing of a multilayer structure, devices maybe fabricated for use with any wavelength and incidence angle. Crystalsalso possess poor mechanical qualities such as resistance to scratching.

X-ray optics has benefitted greatly from three variations on amultilayered optical element: multilayers on figured or curved opticalelements, depth graded multilayers and laterally graded multilayers.

By varying the d spacing laterally across the surface of a figuredoptic, x-rays of the same wavelength can be reflected from every pointon the surface, even where the angle of incidence changes across thesurface. At each point, the angle of incidence and the d spacing ismanipulated according to the Bragg equation. Depth grading is used as ameans for broadening of the band pass, therefore increasing theintegrated reflectivity of a particular multilayer structure.

Two sources of error will profoundly affect the performance of an x-rayoptical element. First, the curvature of the element is difficult toproduce exactly and will be subject to a tolerance range. Second,although great improvements have recently been made in techniques forquality control of evaporated and sputtered films, imperfections in dspacing will always exist.

Errors in the surface curvature of the element will partly destroy theimage. The reflectivity of the element will also decrease because theangle of incidence will be different than that calculated. The d spacingerror will also result in decreased reflectivity.

Accuracy to a fairly low tolerance is required from both the d and θinput in the Bragg equation. However, errors in d spacing are difficultto distinguish from errors in curvature in the final products. Theresult is that numerous elements will probably be discarded before anacceptable optical element is produced. Without the ability to determinewhether the error lies in the shaping or deposition processes, theproduction process cannot be corrected.

The current invention is comprised of a figured optical element andunique methods used to produce a multilayer structure on this element.The optical element consists of a curved substrate upon which aplurality of layer sets are produced. In the production of this element,the causes of imperfections can be isolated and the d spacing and/orangle of incidence can be adjusted to compensate. The result isunprecedented performance of an x-ray optical element.

One method involves characterizing the surface of the optical elementbefore multilayers are deposited onto it. Calculations are thenperformed so that the layer d spacing will compensate for errors in thecurvature. As a result, the reflectivity of the surface will bepreserved.

In an alternate method, a flat optical element will be coated with thinmultilayers whose spacing has been calculated to achieve the desiredeffect on a beam of x-rays for an element with a known curvature. Thenthe deviation of the actual d spacing from the calculated multilayerswill be found. Using this information, an adjusted curvature for anelement can be calculated to compensate for the error in d spacing.

An additional advantage of this invention is its application to x-raysin the soft x-ray (about 10 to 200 angstroms) and the hard x-ray range(about one one-thousandth of an angstrom to 10 angstroms). Previouslydisclosed elements have been limited to use with soft x-rays and extremeultraviolet rays. The appreciably shorter wavelength of hard x-raysdemands previously unattainable accuracy in optical elements.

Proposed applications of such optical elements include spectroscopy anddiffractometry, in particular, a diffractometer using a parabolicmultilayer mirror with lateral grading d spacing which reflects aparallel beam of defined wavelength. Optical elements would also beapplied to focusing optics, for x-ray lithography and microscopy, inparticular, optics for high resolution scanning x-ray microscopy, pointto point imaging optics including multi-element systems, an optic formonochromatization of broad-band radiation, synchrotron radiation inparticular. Many medical applications are also contemplated, inparticular, as power filters to eliminate undesired energy or use inradiography where a high contrast image is desired.

These optical elements can also be used for transformation beams of coldand thermal neutrons. In particular, they can be used for increasingdensity and uniformity of neutron flux or separation of the neutronswith different spin.

Additional objects and advantages of the invention will become apparentfrom the following description and the appended claims when consideredin conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exploded cross-sectional view of a multilayer structurewith uniform layer thicknesses on a substrate;

FIG. 2 illustrates how an optical element, curved in the shape of asection of an elliptical cylinder, which is coated with lateral anddepth graded multilayers, performs line to line imaging;

FIG. 3 is an exploded cross-sectional view of multilayer structure on asubstrate shown in FIG. 2, where the layer thicknesses vary laterallyand by depth;

FIG. 4 illustrates how the curvature of the preferred optical element isin the shape of a section of a parabolic cylinder;

FIG. 5a is a chart showing the accuracy of the curvature produced in twoparabolic mirrors;

FIG. 5b is a graph showing the accuracy of d spacing produced in twoparabolic mirrors;

FIG. 6 illustrates the steps followed in a first method of theinvention;

FIG. 7 illustrates the steps followed in a second method of theinvention;

FIG. 8 illustrates the preferred magnetron sputter deposition assembly;and

FIG. 9 illustrates a Huber diffractometer used to measure the d spacingof multilayers on a flat optical element;

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

With reference to the accompanying drawings, the optical element 2 ofthis invention is shown generally in FIG. 2 and in cross-section in FIG.1 as comprising a substrate 4 coated with a plurality of layer sets.Each layer set 6 is made up of two separate layers of differantmaterials: one with relatively high atomic number, or Z, and a secondwith relatively low atomic number.

FIG. 1 is a cross-sectional view of a multilayer structure, of thicknessd, deposited on a substrate, where x-rays of wavelength λ encounter themultilayer structure with an angle of incidence θ. The multilayers inFIG. 1 are uniform, meaning that the d spacing does not vary eitherlateally or through the depth of the multilayer structure.

One embodiment of an improved optical element with multilayersperforming line to line imaging is illustrated in FIG. 2. The opticalelement 8 pictured in FIG. 2 is shaped as a section of an ellipticalcylinder and has laterally and depth graded multilayers, designed toformat a known shape source to an identically shaped image.

A cross-sectional view of the optical element 11 is shown in FIG. 3,where the cross-section is taken along plane 10 of FIG. 2. The layersets 6 of this optical element 8 are graded lateally and by depth.Lateral grading means that the d spacing varies across the surface ofthe structure. Therefore in FIG. 3:

    d.sub.i <D.sub.i

where i is the order of the layer set and i varies from 1 to n. Themultilayer of FIG. 3 is also depth graded, so the d spacing varies fromlayer to layer. In FIG. 3: where i is the order of the layer set and ivaries from 1 to n.

The layer set thicknesses, or d spacings, of the multilayers

    d.sub.i <d.sub.i+1

    d.sub.i <D.sub.i+1

are on the order of one to a few wavelengths of the desired source. Fromabout 10 to 1000 thin film layers may be deposited on a substrate,depending on the desire qualities of the multilayer structure. The layersets must be composed of two materials with diverse electron densities.The high electron density layer 16 behaves like the plane of atoms in acrystal, while the low electron density layer 18 is analogous to thespace between the planes. In the preferred embodiment of this invention,the heavy element, with a high electron density, is tungsten. Thepreferred choice for the light element, with low electron density, issilicon.

The substrate 4 upon which the multilayers are produced must meetprecise specifications. The surface of substrate 4 must be capable ofbeing polished to roughness which is precise on an atomic level. Theroot mean squared surface roughness of the substrate of the preferredembodiment will range from 0.5 to 20 angstroms, measured at intervals ofabout 10 angstroms. Examples of material used for substrates are siliconwafers, mica, quartz, zeradot, sapphire, germanium, pyrex, siliconcarbide or other like substances. In the preferred embodiment of thisinvention, the substrate is a silicon <100> wafer. A <100>-orientedsilicon crystal exposes a smaller number of incomplete interatomic bondsat the crystal surface than a <111>-oriented crystal.

The curvature of the substrate 4 may take the form of a section of anelliptical cylinder, a parabolic cylinder or an aspherical surface. FIG.4 illustrates how the surface 20 of a cross-section of a substratemimics the curvature of a section of a parabola 22. This surface 20 isdesigned to format the incident x-rays into a collimated beam of x-rays.

For the most precise applications, the substrate is ground to the propercurvature and then polished on an atomic level. Alternatively, thesubstrate is attached to a rigid curved metallic piece by a layer ofadhesive. When adhesive is used, the substrate is an extremely thin,elastically bendable substance. The adhesive used, preferably some formof an epoxy, must not expand or contract within a very precise tolerancerange. The adhesive may also serve the purpose of leveling off theoptical element by filling in any uneven areas.

The steps of a first method of this invention, diagrammed in FIG. 6,isolate the error in the curvature of the surface before multilayers aredeposited, and then compensate for the error by adjusting the layer dspacing. First, a workable d spacing scheme and optical elementcurvature for the desired wavelength and contemplated use is calculatedby using the Bragg equation. Next, the substrate is ground to thecalculated curvature and polished on an atomic level. The deviation ofthe actual curvature from the calculated curvature is then measuredusing known techniques. The Bragg equation is again utilized tocalculate new d spacings for the multilayers which will compensate forthe error in the actual curvature. Finally, multilayers on the curvedsubstrate are produced with the compensating d spacing.

A second alternate process is diagrammed in FIG. 7. First the required dspacings and curvature are calculated using the Bragg equation. Then aflat optical element is coated with thin multilayers whose spacing hasbeen calculated to achieve the desired effect on a beam of x-rays for anelement with the calculated curvature. Next, the deviation of the actuald spacing from the calculated d spacing will be found. Using thisinformation, the Bragg equation is used to calculate an adjustedcurvature for the element which compensates for the deviation of the dspacing. The coated substrate is then shaped to the compensatingcurvature.

Alternatively, in the second method an optical element can be producedwith the desired curvature and coating instead of coating a flatelement. This curved coated element may then be flattened in order tocharacterized the d spacing of the layers. Although layers on a curvedoptical element can be characterized without flattening, flattening theelement is the simplest method.

Many different techniques can be used to produce the multilayers on thesubstrate, including magnetron sputtering, electron-beam deposition, andlaser evaporation. A rotating drum type magnetron sputtering system 28is shown at FIG. 8. The substrate 4 is placed on a rotating drum 30. Acoating material 32, attached to a cathode 34, is bombarded byparticles. Atomic particles are then dislodged from the coating material32 and are intercepted by the substrate 4. One of two coating materials32 is placed on each cathode 34, where the cathodes are located about160° apart. The drum 30 rotates with an angular velocity, exposing thesubstrate 4 to a coating material 32 as it passes each cathode 34. Onelayer set is deposited in one rotation.

The substrate 4 is mounted on a spinning platform 36 which is in turnmounted on the rotating drum 30. The platform 36 spins, with a knownangular velocity, on an axis perpendicular to the axis of the drum 30.

Lateral grading of the multilayer is accomplished by mounting a maskbetween the cathode 34 and the substrate 4. The mask 38 is preciselyshaped to accomplish the desired laterally graded layer as the substrate4 rotates. Depth grading is achieved by varying the angular velocity ofthe rotating drum 30, thereby varying the amount of coating material 32which will fall upon the substrate 4 in each rotation.

The d spacings of layers on a flat optical element are characterizedusing the Huber diffractometer illustrated in FIG. 9. This instrumentcan precisely characterize the multilayer structure in a very smallarea. Numerous measurements are necessary to examine the entiremultilayer structure. The radiation coming from the x-ray tube 40 is abeam of Copper K-α radiation 42, which is reflected off a Germanium<111> monochromator 44. The collimation of the beam is determined byadjusting two collimating slits 46 in the primary beam path. Thesubstrate 4 is translated across the x-ray beam 42 in the directionnormal to the optical axis of the apparatus. The substrate 4 is alsorotated in the direction of arrow 50. After being diffracted by themultilayers, the beam passes through a receiving slit 52 and into adetector 54 which measures the intensity of the radiation received. Asthe substrate is rotated through an angle φ along arrow 50, the detectoris rotated through twice the angle, 2φ, in the direction of arrow 56.The aggregate instrumental error of the diffractometer used is less than0.1%.

Both of the above described methods are iterative processes, which canbe repeated and used in combination until the required performance levelof the optical element is achieved. FIG. 5a shows the accuracy, inarcminutes, achieved for the curvature of two multilayer mirrors whichwere tested. These multilayer mirrors, piece 1 and piece 2, were curvedin the shape of a parabolic cylinder. FIG. 5b is a graph which shows theaccuracy of the layer set d spacings on the same two multilayer mirrors.The straight line on the graph shows the desired theoretical d spacingsin angstroms plotted against the length position on the multilayerstructure in millimeters.

While the above description constitutes the preferred embodiments of thepresent invention, it will be appreciated that the invention issusceptible of modification, variation and change without departing fromthe proper scope and fair meaning of the accompanying claims.

What is claimed:
 1. A method for producing a figured optical elementwith multilayers in order to diffract x-rays comprising the steps of:a.theoretically calculating workable d space gradings of multilayercoatings and substrate curvature for contemplated use by using the Braggequation; b. shaping the substrate to the calculated curvature; c.measuring the deviation of the substrate curvature from the calculatedcurvature; d. using the Bragg equation to calculate new d spacings forthe multilayers which would compensate for the error in the substratecurvature; and e. producing multilayers on the curved substrate with thecompensating d spacing.
 2. The method of claim 1 where the multilayersare produced on the curved substrate using magnetron sputteringdeposition.
 3. The method of claim 1 wherein said substrate is shaped bybeing ground to said known curvature and then polished.
 4. The method ofclaim 1 where said substrate is a thin flexible layer which is shaped bybeing adhered to a rigid piece having said known curvature.
 5. A methodfor producing a figured optical element comprising a substrate withmultilayer coatings in order to diffract x-rays comprising the stepsof:a. theoretically calculating the workable d space gradings ofmultilayer coatings and substrate curvature for contemplated use byusing the Bragg equation; b. producing multilayer coatings with thecalculated d spacings on a flat substrate; c. measuring the deviation ofthe d spacings of the multilayer coatings on the flat substrate from thecalculated d spacings; d. calculating a new curvature for the substrateusing the Bragg equation which will compensate for the deviation of theactual d spacing from the calculated d spacing; e. shaping the substratewith the compensating curvature so as to improve the performance of theoptical element.
 6. The method of claim 5 where said substrate is shapedby being ground to said known curvature and then polished.
 7. The methodof claim 5 where said substrate is thin flexible layer which is shapedby being adhered to a rigid piece having said known curvature.
 8. Themethod of claim 5 where the multilayers are produced on the curvedsubstrate using magnetron sputtering deposition.